The New Yorker had a great article, titled Numbers Guy. The author, Jim Holt, wrote about the brain research into how humans experience and work with numbers. There are alot of interesting data here, including how it seems that there are two parts to the brain, one doing rough approximation, and a separate part doing precise ordering and calculation. Stanislas Dehaene, a neuroscientist in Paris, was working with a subject who had sustained a brain hemorrhage that left him with an enormous lesion in the rear half of his brain’s left hemisphere:

Dehaene….showed him the numerals 7 and 8. Mr. N was able to answer quickly that 8 was the larger number—far more quickly than if he had had to identify them by counting up to the right quantities. He could also judge whether various numbers were bigger or smaller than 55, slipping up only when they were very close to 55. Dehaene dubbed Mr. N “the Approximate Man.” The Approximate Man lived in a world where a year comprised “about 350 days” and an hour “about fifty minutes,” where there were five seasons, and where a dozen eggs amounted to “six or ten.” Dehaene asked him to add 2 and 2 several times and received answers ranging from three to five. But, he noted, “he never offers a result as absurd as 9.”

Somehow, the damaged part of the subject’s brain had taken away his ability to do precise number handling, but the rough approximation function is in some other part of the brain and it’s left intact.

To me, the most interesting observations about the article has to do with bilingualism, as I’m bilingual (more precisely semi-bi-lingual since my Chinese has regressed so much, which would make me more of a “lingual”). In particular:

- To this day when I have to multiply in my head, I recite the Chinese multiplication table because that’s how I learned it. This is different from addition, which I do without having to think in terms of linguistic languages. Dehaene’s research confirms my own observation, in that multiplication, unlike addition, is “unnatural practice” because our brains are wired exactly wrong for it, whereas there’s evidence that addiction activity is evident even in babies who haven’t acquired language skills. Since there is no neurological circuitry for multiplication, all of us has to memorize the multiplication table verbally, as a string of words.
- Similar to multiplication, but to a lesser degree, I tend to remember long series of numbers in Chinese, specifically in Cantonese. I thought it was the same phenomenon as the multiplication table, because I learned to count in Chinese. But Dehaene noted that linguistically Chinese number words are just more brief, and take less than a quarter of a second to say compared to a third of a second for English. This resulted in the average Chinese speaker has a memory span of nine digits vs seven for English speakers. And apparently, the Cantonese dialet is even more efficient in that Hong Kong people can juggle ten digits with no problem. Who knew I have been enjoying a cultural advantage all along!
- My three year old is learning to count, but she frequently counts “…13, 14, 16, 17…” I had concluded that “fifteen” doesn’t follow the “-teen” rule, in that it doesn’t sound like “four-teen” or “six-teen” and was causing her problem. Turns out that my hunch is correct. Dehane has noted that we use special words for numbers from 11 to 19, and for decades 20-90, and thus it’s more challenging to learn to count in English. (French is even worse, working in base of 20, so 98 is “four twenty ten nine.” That explains so much about the French :-)) Not only that, Chinese is great for counting, because it’s modular, in that all the digits are based on ten. So 54 is “five-ten-four” and 291 is “two-hundred-nine-ten-one”. And the sound for “hundred” “thousand” “million” and so on are all single syllable, so it’s easy to say as well. Dehaene believes that this is one of the reasons why the Asian students are better at math than Western students.

So maybe I better gear up to teach my kids math in Chinese so they can sustain an advantage in math over her friends :-)

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